RealRooted.lean

import RealRooted.ASWCubicCharacteristic
import RealRooted.ASWCubicClosedForm
import RealRooted.ASWCubicClosedFormAdapter
import RealRooted.ASWCubicDegreeThree
import RealRooted.ASWCubicDominance
import RealRooted.ASWCubicEqualModulus
import RealRooted.ASWCubicMinors
import RealRooted.ASWCubicNonrealFactor
import RealRooted.ASWCubicRecurrence
import RealRooted.ASWKarlinKernel
import RealRooted.ASWKarlinMatrix
import RealRooted.ASWKarlinSineBounds
import RealRooted.ASWKarlinThreshold
import RealRooted.ASWKarlinVariation
import RealRooted.ASWKarlinVectors
import RealRooted.AffineDerivative
import RealRooted.AffineFamily
import RealRooted.AissenSchoenbergWhitney
import RealRooted.AissenSchoenbergWhitneyBase
import RealRooted.AllCombo
import RealRooted.Apolarity
import RealRooted.Basic
import RealRooted.Bezoutian
import RealRooted.BoundarySpecializationRight
import RealRooted.BorceaBranden.BoundarySpecialization
import RealRooted.BorceaBranden.FiniteSymbolCoefficient
import RealRooted.BorceaBranden.FiniteSymbolContraction
import RealRooted.BorceaBranden.FiniteSymbolDegree
import RealRooted.BorceaBranden.FiniteSymbolLinearity
import RealRooted.BorceaBranden.FiniteSymbolPreserver
import RealRooted.BorceaBranden.FiniteSymbolProduct
import RealRooted.BorceaBranden.FiniteSymbolReciprocal
import RealRooted.BorceaBranden.FiniteSymbolReconstruction
import RealRooted.BorceaBranden.FiniteSymbolReconstructionCore
import RealRooted.BorceaBranden.FiniteSymbolBasis
import RealRooted.BorceaBranden.Applications.BidiagonalSymbol
import RealRooted.BorceaBranden.Applications.HomogenizeStable
import RealRooted.BorceaBranden.Applications.UnivariateSymbol
import RealRooted.CauchyInterlacing
import RealRooted.Challenges.AissenSchoenbergWhitney
import RealRooted.Challenges.BorceaBranden
import RealRooted.Challenges.BrandenSolus
import RealRooted.Challenges.BraunJal
import RealRooted.Challenges.CauchyInterlacing
import RealRooted.Challenges.ChudnovskySeymour
import RealRooted.Challenges.Eulerian
import RealRooted.Challenges.Favard
import RealRooted.Challenges.Hadamard
import RealRooted.Challenges.HermiteBiehlerHurwitz
import RealRooted.Challenges.HermitePoulain
import RealRooted.Challenges.HosterStump
import RealRooted.Challenges.Issue34SingleMatrixCounterexample
import RealRooted.Challenges.Issue34WindowObstruction
import RealRooted.Challenges.Kurtz
import RealRooted.Challenges.MatrixInterlacing
import RealRooted.Challenges.Obreschkoff
import RealRooted.Challenges.OperatorPreservers
import RealRooted.Challenges.VeroneseSections
import RealRooted.Challenges.Wagner
import RealRooted.ChudnovskySeymour
import RealRooted.ClosedSegmentCountEqFromAnalytic
import RealRooted.CoefficientShape
import RealRooted.CombinatorialExamples
import RealRooted.CombinatorialExamples.BigDescentsOddBinom
import RealRooted.CombinatorialExamples.ColoredSetPartitions
import RealRooted.CombinatorialExamples.Common
import RealRooted.CombinatorialExamples.Eulerian
import RealRooted.CombinatorialExamples.Motzkin
import RealRooted.CombinatorialExamples.Narayana
import RealRooted.CombinatorialExamples.OneDescentGamma
import RealRooted.CombinatorialExamples.Simsun
import RealRooted.CombinatorialExamples.SingletonFreeSetPartitions
import RealRooted.CombinatorialExamples.StirlingPermutations
import RealRooted.CombinatorialExamples.SturmDerangementsExc
import RealRooted.CombinatorialExamples.Touchard
import RealRooted.CombinatorialExamples.TypeBEulerian
import RealRooted.Combinatorics.OrderedSubsetPairsNarayana
import RealRooted.CommonInterleaver.AffineBoundary
import RealRooted.CommonInterleaver.IntervalLemmas
import RealRooted.CommonInterleaver.PairBridge
import RealRooted.CommonInterleaver.PairwiseUpgrade
import RealRooted.CommonInterleaver.RightPencil
import RealRooted.CommonInterleaver.RootCountCombinatorics
import RealRooted.CommonInterleaver.SameDegreeRootCount
import RealRooted.CommonInterleaver.Statements
import RealRooted.CommonInterleaver.SuccDegreeEndpoint
import RealRooted.CommonInterleaver.SuccDegreeLowDegree
import RealRooted.CommonInterleaverExamples
import RealRooted.CommonInterleaverSeq
import RealRooted.CommonInterleaverTwo
import RealRooted.Compatibility.Basic
import RealRooted.Compatibility.InterleaverBridge
import RealRooted.ComplexCesaro
import RealRooted.ComplexPowers
import RealRooted.ConvexCombination
import RealRooted.CubicDiscriminant
import RealRooted.CubicNewton
import RealRooted.DegreeDropDivXPrec
import RealRooted.DegreeDropReversal
import RealRooted.DegreeIncreasingLocalLowerCount
import RealRooted.Derivative
import RealRooted.DifferentialBlocks
import RealRooted.ElementaryDifferential
import RealRooted.EulerOperator
import RealRooted.Favard
import RealRooted.FolkloreLemma
import RealRooted.GammaRealRoots
import RealRooted.GarloffWagner
import RealRooted.GeneralizedLiuWang
import RealRooted.GeneralizedSnakePosets
import RealRooted.GeneralizedSnakePosets.FiniteBoard
import RealRooted.GeneralizedSnakePosets.MatrixInduction
import RealRooted.GeneralizedSnakePosets.Narayana.Claim7
import RealRooted.GeneralizedSnakePosets.Narayana.JacobiTransport
import RealRooted.GeneralizedSnakePosets.Narayana.Modified
import RealRooted.GeneralizedSnakePosets.Narayana.Turan
import RealRooted.GeneralizedSnakePosets.Narayana.TuranCertificates
import RealRooted.GeneralizedSnakePosets.Section3Packages
import RealRooted.GeneralizedSnakePosets.SnakeBoard
import RealRooted.GeneralizedSnakePosets.SnakeCover
import RealRooted.GeneralizedSnakePosets.SnakeReachability
import RealRooted.GeneralizedSnakePosets.SnakeStaircase
import RealRooted.GeneralizedSnakePosets.SnakeWord
import RealRooted.GeneralizedSnakePosets.SquarecaseModel
import RealRooted.GeneralizedSnakePosets.Statements
import RealRooted.GeneralizedSnakePosets.TruncatedStaircase
import RealRooted.GeneralizedSnakePosetsNarayana
import RealRooted.GraceHalfPlane
import RealRooted.GustafssonSolus
import RealRooted.Hadamard
import RealRooted.HadamardProduct
import RealRooted.HeilmannLieb
import RealRooted.HermiteBiehler
import RealRooted.HurwitzMatrix
import RealRooted.InterlacingSequence
import RealRooted.InterlacingSequenceBasic
import RealRooted.IteratedDerivativeShift
import RealRooted.LiebSokal
import RealRooted.LiebSokalOperator
import RealRooted.LiebSokalPointwise
import RealRooted.Linear
import RealRooted.LinearPowerFamily
import RealRooted.LiuOppositeSigns
import RealRooted.LiuOppositeSigns.CommonInterleaverConsequences
import RealRooted.LiuOppositeSigns.Corollary22
import RealRooted.LiuOppositeSigns.DeletionBranches
import RealRooted.LiuOppositeSigns.FactorReturnAssembly
import RealRooted.LiuOppositeSigns.FactorReturnLeft
import RealRooted.LiuOppositeSigns.FactorReturnStatements
import RealRooted.LiuOppositeSigns.FactorReturnTwoDegree
import RealRooted.LiuOppositeSigns.ForwardCubicLinear
import RealRooted.LiuOppositeSigns.ForwardCubicQuadratic.Average
import RealRooted.LiuOppositeSigns.ForwardCubicQuadratic.LowerSideDouble
import RealRooted.LiuOppositeSigns.ForwardCubicQuadratic.LowerSideStrict
import RealRooted.LiuOppositeSigns.ForwardCubicQuadratic.MiddleGap
import RealRooted.LiuOppositeSigns.ForwardCubicQuadratic.RightProtruding
import RealRooted.LiuOppositeSigns.ForwardCubicQuadratic.RootOrderAssembly
import RealRooted.LiuOppositeSigns.ForwardCubicQuadratic.RootOrderLower
import RealRooted.LiuOppositeSigns.ForwardCubicQuadratic.RootOrderMiddle
import RealRooted.LiuOppositeSigns.ForwardCubicQuadratic.RootOrderStatement
import RealRooted.LiuOppositeSigns.ForwardCubicQuadratic.RootOrderUpper
import RealRooted.LiuOppositeSigns.ForwardLowDegree
import RealRooted.LiuOppositeSigns.NonnegCoeffs
import RealRooted.LiuOppositeSigns.PositiveSplitPair
import RealRooted.LiuOppositeSigns.Theorem21Assembly
import RealRooted.LiuOppositeSigns.Theorem21Statements
import RealRooted.LiuOppositeSigns.XSub.CubicCubic
import RealRooted.LiuOppositeSigns.XSub.CubicQuadratic
import RealRooted.LiuOppositeSigns.XSub.IntervalRootCount
import RealRooted.LiuOppositeSigns.XSub.LeftSucc
import RealRooted.LiuOppositeSigns.XSub.LeftSuccDegreeThree
import RealRooted.LiuOppositeSigns.XSub.LeftSuccDegreeTwo
import RealRooted.LiuOppositeSigns.XSub.LinearQuadratic
import RealRooted.LiuOppositeSigns.XSub.QuadraticCubic
import RealRooted.LiuOppositeSigns.XSub.QuadraticQuadratic
import RealRooted.LiuOppositeSigns.XSub.QuarticCubic
import RealRooted.LiuOppositeSigns.XSub.QuarticCubicBoundary
import RealRooted.LiuOppositeSigns.XSub.QuarticCubicCommonRoot
import RealRooted.LiuOppositeSigns.XSub.SameDegree
import RealRooted.LiuOppositeSigns.XSub.SplittingTools
import RealRooted.LiuOppositeSignsTheorem
import RealRooted.LiuWangBenchmark
import RealRooted.LiuWangRecursion
import RealRooted.LowerTriangularMatrix
import RealRooted.MaWang
import RealRooted.MagnitudeDominated
import RealRooted.MaoWangMatrixProduct
import RealRooted.Mathlib.Algebra.MvPolynomial.Stability.DegreeBox
import RealRooted.Mathlib.Algebra.MvPolynomial.Stability.Symbol
import RealRooted.Mathlib.Algebra.Polynomial.Basic
import RealRooted.Mathlib.Algebra.Polynomial.Degree.Operations
import RealRooted.Mathlib.Algebra.Polynomial.Derivative
import RealRooted.Mathlib.Algebra.Polynomial.Eval.Defs
import RealRooted.Mathlib.Algebra.Polynomial.Homogenize
import RealRooted.Mathlib.Algebra.Polynomial.Roots
import RealRooted.Mathlib.Algebra.Polynomial.Splits
import RealRooted.Mathlib.Analysis.Complex.OpenMapping
import RealRooted.Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
import RealRooted.Mathlib.Combinatorics.Enumerative.OrderedSubsetPairs
import RealRooted.Mathlib.Data.List.Interleave
import RealRooted.Mathlib.Data.List.Zip
import RealRooted.Mathlib.Data.Nat.Cast.Basic
import RealRooted.Mathlib.Data.Nat.Choose.Cast
import RealRooted.Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import RealRooted.Mathlib.LinearAlgebra.Matrix.KernelSignVariation
import RealRooted.Mathlib.LinearAlgebra.Matrix.SignVariation
import RealRooted.Mathlib.LinearAlgebra.Matrix.TotallyNonneg
import RealRooted.Mathlib.LinearAlgebra.Matrix.VariationDiminishing
import RealRooted.MatrixInterlacing
import RealRooted.MultiaffineReciprocalRight
import RealRooted.Multiaffine
import RealRooted.MultiaffineReciprocal
import RealRooted.MultiplierSequence
import RealRooted.MultivariateStability
import RealRooted.NarayanaTransformation
import RealRooted.NewtonAux
import RealRooted.OEIS.A046802
import RealRooted.ObreschkoffContinuity
import RealRooted.ObreschkoffConverse
import RealRooted.OperatorPreservesInterlacing
import RealRooted.PFPolynomial
import RealRooted.Polarization
import RealRooted.PolyaFrequencyConvolution
import RealRooted.PosCombo
import RealRooted.PositiveParameterLocalLowerCount
import RealRooted.ProductFamily
import RealRooted.QuadraticCubicPencil
import RealRooted.QuadraticRoot
import RealRooted.RectangularConvolution
import RealRooted.RectangularConvolutionIdentity
import RealRooted.RectangularPolarization
import RealRooted.RectangularPolarizationComplement
import RealRooted.RecurrenceDiscriminant
import RealRooted.RootContinuity
import RealRooted.RootCountFinite
import RealRooted.RootCountJump
import RealRooted.RootCountLocalConstancy
import RealRooted.RootMultiplicityMatching
import RealRooted.RootOrderBridge
import RealRooted.RootSumBounds
import RealRooted.RowThreshold
import RealRooted.SameDegreeCountFromAnalytic
import RealRooted.SameDegreeCubicRootCount
import RealRooted.SameDegreeCubicSecondRootFromAnalytic
import RealRooted.SameDegreeDerivative
import RealRooted.SameDegreeMultiplicityLowerCount
import RealRooted.SameDegreeQuadraticObstruction
import RealRooted.SameDegreeQuadraticRootCount
import RealRooted.ShiftLemma
import RealRooted.SmallPositiveParameterCount
import RealRooted.StaircaseSum
import RealRooted.SuccDegreeLeftEndpoint
import RealRooted.SuccDegreeRootCrossing
import RealRooted.SymmetricDecomposition
import RealRooted.Tactic
import RealRooted.Tactic.AffineDerivative
import RealRooted.Tactic.AissenSchoenbergWhitney
import RealRooted.Tactic.AllCombo
import RealRooted.Tactic.Attr
import RealRooted.Tactic.Bezoutian
import RealRooted.Tactic.CoefficientShape
import RealRooted.Tactic.CommonInterleaver
import RealRooted.Tactic.CubicDiscriminant
import RealRooted.Tactic.Derivative
import RealRooted.Tactic.EulerOperator
import RealRooted.Tactic.Examples
import RealRooted.Tactic.Examples.AffineDerivative
import RealRooted.Tactic.Examples.AissenSchoenbergWhitney
import RealRooted.Tactic.Examples.AllCombo
import RealRooted.Tactic.Examples.Attr
import RealRooted.Tactic.Examples.Bezoutian
import RealRooted.Tactic.Examples.CoefficientShape
import RealRooted.Tactic.Examples.Combinatorial
import RealRooted.Tactic.Examples.CommonInterleaver
import RealRooted.Tactic.Examples.CubicDiscriminant
import RealRooted.Tactic.Examples.Derivative
import RealRooted.Tactic.Examples.EulerOperator
import RealRooted.Tactic.Examples.Favard
import RealRooted.Tactic.Examples.Finish
import RealRooted.Tactic.Examples.FiniteSymbol
import RealRooted.Tactic.Examples.FiniteSymbolPF
import RealRooted.Tactic.Examples.FiniteSymbolPFFrontend
import RealRooted.Tactic.Examples.GammaRealRoots
import RealRooted.Tactic.Examples.Hadamard
import RealRooted.Tactic.Examples.HermiteBiehler
import RealRooted.Tactic.Examples.HermitePoulain
import RealRooted.Tactic.Examples.HomogenizeStable
import RealRooted.Tactic.Examples.I2DerivativeLag
import RealRooted.Tactic.Examples.InterlacingSequence
import RealRooted.Tactic.Examples.IteratedDerivativeShift
import RealRooted.Tactic.Examples.IteratedDerivativeShiftProduct
import RealRooted.Tactic.Examples.J1Chebyshev
import RealRooted.Tactic.Examples.J1Gap3Reciprocal
import RealRooted.Tactic.Examples.Kurtz
import RealRooted.Tactic.Examples.Linear
import RealRooted.Tactic.Examples.LinearPowerFamily
import RealRooted.Tactic.Examples.LiuWang
import RealRooted.Tactic.Examples.LiuWangRecursion
import RealRooted.Tactic.Examples.Lookup
import RealRooted.Tactic.Examples.MaWang
import RealRooted.Tactic.Examples.MagnitudeDominated
import RealRooted.Tactic.Examples.Matrix
import RealRooted.Tactic.Examples.MultiplierSequence
import RealRooted.Tactic.Examples.Narayana
import RealRooted.Tactic.Examples.OEIS
import RealRooted.Tactic.Examples.OEISPositiveTLag
import RealRooted.Tactic.Examples.OEISTestbed
import RealRooted.Tactic.Examples.OperatorPreservesInterlacing
import RealRooted.Tactic.Examples.PFBidiagonal
import RealRooted.Tactic.Examples.PFBidiagonalFrontend
import RealRooted.Tactic.Examples.PFPolynomial
import RealRooted.Tactic.Examples.PosCombo
import RealRooted.Tactic.Examples.PreservingOperatorSequence
import RealRooted.Tactic.Examples.Product
import RealRooted.Tactic.Examples.RecurrenceIdentification
import RealRooted.Tactic.Examples.ReciprocalShift
import RealRooted.Tactic.Examples.RootBounds
import RealRooted.Tactic.Examples.RootCount
import RealRooted.Tactic.Examples.ScalarDen
import RealRooted.Tactic.Examples.SecondDerivative
import RealRooted.Tactic.Examples.SequenceSurvey
import RealRooted.Tactic.Examples.SideGoals
import RealRooted.Tactic.Examples.Sign
import RealRooted.Tactic.Examples.SignAssembly
import RealRooted.Tactic.Examples.StaircaseSum
import RealRooted.Tactic.Examples.SymmetricDecomposition
import RealRooted.Tactic.Examples.VeroneseSection
import RealRooted.Tactic.Examples.Wagner
import RealRooted.Tactic.Examples.WagnerX
import RealRooted.Tactic.Examples.WeightedSum
import RealRooted.Tactic.Favard
import RealRooted.Tactic.Finish
import RealRooted.Tactic.FiniteSymbol
import RealRooted.Tactic.FiniteSymbolPF
import RealRooted.Tactic.FiniteSymbolPFFrontend
import RealRooted.Tactic.GammaRealRoots
import RealRooted.Tactic.Hadamard
import RealRooted.Tactic.HermiteBiehler
import RealRooted.Tactic.HermitePoulain
import RealRooted.Tactic.HomogenizeStable
import RealRooted.Tactic.I2DerivativeLag
import RealRooted.Tactic.InterlacingSequence
import RealRooted.Tactic.IteratedDerivativeShift
import RealRooted.Tactic.IteratedDerivativeShiftProduct
import RealRooted.Tactic.J1Chebyshev
import RealRooted.Tactic.J1Gap3Reciprocal
import RealRooted.Tactic.Kurtz
import RealRooted.Tactic.Linear
import RealRooted.Tactic.LinearPowerFamily
import RealRooted.Tactic.LiuWang
import RealRooted.Tactic.LiuWangRecursion
import RealRooted.Tactic.Lookup
import RealRooted.Tactic.MaWang
import RealRooted.Tactic.MagnitudeDominated
import RealRooted.Tactic.Matrix
import RealRooted.Tactic.MultiplierSequence
import RealRooted.Tactic.Narayana
import RealRooted.Tactic.OEIS
import RealRooted.Tactic.OperatorPreservesInterlacing
import RealRooted.Tactic.PFBidiagonal
import RealRooted.Tactic.PFBidiagonalFrontend
import RealRooted.Tactic.PFPolynomial
import RealRooted.Tactic.PosCombo
import RealRooted.Tactic.PreservingOperatorSequence
import RealRooted.Tactic.Product
import RealRooted.Tactic.RecurrenceIdentification
import RealRooted.Tactic.ReciprocalShift
import RealRooted.Tactic.RootBounds
import RealRooted.Tactic.RootCount
import RealRooted.Tactic.ScalarDen
import RealRooted.Tactic.SecondDerivative
import RealRooted.Tactic.SideGoals
import RealRooted.Tactic.Sign
import RealRooted.Tactic.SignAssembly
import RealRooted.Tactic.StaircaseSum
import RealRooted.Tactic.SymmetricDecomposition
import RealRooted.Tactic.Targets
import RealRooted.Tactic.VeroneseSection
import RealRooted.Tactic.Wagner
import RealRooted.Tactic.WagnerX
import RealRooted.Tactic.WeightedSum
import RealRooted.ThresholdMatrix
import RealRooted.Touchard
import RealRooted.TridiagonalDet
import RealRooted.UpperDerivativeInterlace
import RealRooted.VeroneseMatrix
import RealRooted.VeroneseSection
import RealRooted.Wagner
import RealRooted.WagnerLeftSum
import RealRooted.WagnerRightSum
import RealRooted.WagnerX
import RealRooted.WeightedSum